Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 4 & 8 & 2 & 8 \\
4 & 1 & 4 & 8 & 2 & 8 \\
4 & 4 & 1 & 2 & 2 & 2 \\
8 & 8 & 2 & 1 & 4 & 4 \\
2 & 2 & 2 & 4 & 1 & 4 \\
8 & 8 & 2 & 4 & 4 & 1
\end{array}\right)\)
Elliptic curves in class 11.1-b over 4.4.7625.1
Isogeny class 11.1-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 11.1-b1
| \( \bigl[a^{2} - 5\) , \( \frac{1}{4} a^{3} - \frac{5}{4} a^{2} + \frac{3}{4} a + 5\) , \( a^{2} - a - 5\) , \( \frac{5}{2} a^{3} - \frac{15}{2} a^{2} - \frac{5}{2} a + 18\) , \( \frac{13}{4} a^{3} - \frac{41}{4} a^{2} - \frac{17}{4} a + 22\bigr] \)
|
| 11.1-b2
| \( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a + 1\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 4\) , \( 26 a^{3} + 21 a^{2} - 193 a - 234\) , \( -121 a^{3} - 57 a^{2} + 1049 a + 1221\bigr] \)
|
| 11.1-b3
| \( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( -\frac{1}{4} a^{3} + \frac{5}{4} a^{2} - \frac{3}{4} a - 6\) , \( a + 1\) , \( -\frac{3}{2} a^{3} - \frac{9}{2} a^{2} + \frac{15}{2} a + 16\) , \( \frac{25}{4} a^{3} + \frac{39}{4} a^{2} - \frac{81}{4} a - 30\bigr] \)
|
| 11.1-b4
| \( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( -\frac{1}{4} a^{3} + \frac{5}{4} a^{2} - \frac{3}{4} a - 6\) , \( a + 1\) , \( -\frac{111}{4} a^{3} - \frac{153}{4} a^{2} + \frac{335}{4} a + 116\) , \( \frac{1063}{4} a^{3} + \frac{2365}{4} a^{2} - \frac{3471}{4} a - 1594\bigr] \)
|
| 11.1-b5
| \( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( -\frac{1}{4} a^{3} - \frac{3}{4} a^{2} + \frac{9}{4} a + 5\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 5\) , \( -\frac{83}{4} a^{3} + \frac{183}{4} a^{2} + \frac{487}{4} a - 229\) , \( \frac{403}{4} a^{3} - \frac{951}{4} a^{2} - \frac{2351}{4} a + 1201\bigr] \)
|
| 11.1-b6
| \( \bigl[1\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 4\) , \( a + 1\) , \( -\frac{3}{4} a^{3} + \frac{7}{4} a^{2} + \frac{43}{4} a - 19\) , \( -\frac{23}{4} a^{3} + \frac{67}{4} a^{2} + \frac{91}{4} a - 62\bigr] \)
|
